不变空间树网络中的路由长度

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2021-03-01 DOI:10.1214/21-ECP401

D. Aldous

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引用次数: 0

摘要

是否存在常数r0，使得在连接平面中比率为1的泊松点的任何不变树网络中，对于r>r0，欧几里得距离r处的点之间的平均网络内距离是无限的？我们证明了一个稍微较弱的结果。这是Benjamini等人（2001）关于整数格的不变生成树的结果的连续体模拟。

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Route lengths in invariant spatial tree networks

Is there a constant r0 such that, in any invariant tree network linking rate-1 Poisson points in the plane, the mean within-network distance between points at Euclidean distance r is infinite for r>r0? We prove a slightly weaker result. This is a continuum analog of a result of Benjamini et al (2001) on invariant spanning trees of the integer lattice.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.